u3 t2 regla de la cadena trigonometricas
TRANSCRIPT
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Derivadas
Santiago Moll Lpez
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Objetivos:
IAplicar la regla de la cadena al clculo de
derivadas
IRepasar las derivas de algunas funciones
trigonomtricas
Requisitos:
IConocer las derivadas de las funciones
elementales
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Objetivos:
IAplicar la regla de la cadena al clculo de
derivadas
IRepasar las derivas de algunas funciones
trigonomtricas
Requisitos:
IConocer las derivadas de las funciones
elementales
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Regla de la Cadena:
I
f (x) = sin(g(x)) f (x) = cos(g(x)) g (x)
I
f (x) = cos(g(x)) f (x) =sin(g(x)) g (x)
I
f (x) = tan(g(x)) f (x) = (1+ tan2(g(x))) g (x)
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Regla de la Cadena:
If (x) = sin(g(x))
f (x) = cos(g(x)) g (x)
I
f (x) = cos(g(x)) f (x) =sin(g(x)) g (x)
I
f (x) = tan(g(x)) f (x) = (1+ tan2(g(x))) g (x)
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Regla de la Cadena:
If (x) = sin(g(x)) f (x) = cos(g(x)) g (x)
I
f (x) = cos(g(x)) f (x) =sin(g(x)) g (x)
I
f (x) = tan(g(x)) f (x) = (1+ tan2(g(x))) g (x)
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Regla de la Cadena:
If (x) = sin(g(x)) f (x) = cos(g(x)) g (x)
If (x) = cos(g(x))
f (x) =sin(g(x)) g (x)
I
f (x) = tan(g(x)) f (x) = (1+ tan2(g(x))) g (x)
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Regla de la Cadena:
If (x) = sin(g(x)) f (x) = cos(g(x)) g (x)
If (x) = cos(g(x)) f (x) =sin(g(x)) g (x)
I
f (x) = tan(g(x)) f (x) = (1+ tan2(g(x))) g (x)
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Regla de la Cadena:
If (x) = sin(g(x)) f (x) = cos(g(x)) g (x)
If (x) = cos(g(x)) f (x) =sin(g(x)) g (x)
If (x) = tan(g(x))
f (x) = (1+ tan2(g(x))) g (x)
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Regla de la Cadena:
If (x) = sin(g(x)) f (x) = cos(g(x)) g (x)
If (x) = cos(g(x)) f (x) =sin(g(x)) g (x)
If (x) = tan(g(x)) f (x) = (1+ tan2(g(x))) g (x)
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Ejemplos:
f (x) = sin(g(x)) f (x) = cos(g(x)) g (x)
I
f (x) = sin(x2+3x+8) f (x) = cos(x2+3x+8) (2x+3)
I
f (x) = sin(ex + x3) f (x) = cos(ex + x3) (ex +3x2)
I
f (x) = sin(ln(x)) f (x) = cos(ln(x)) 1x
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Ejemplos:
f (x) = sin(g(x))
f (x) = cos(g(x)) g (x)
I
f (x) = sin(x2+3x+8) f (x) = cos(x2+3x+8) (2x+3)
I
f (x) = sin(ex + x3) f (x) = cos(ex + x3) (ex +3x2)
I
f (x) = sin(ln(x)) f (x) = cos(ln(x)) 1x
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Ejemplos:
f (x) = sin(g(x)) f (x) = cos(g(x)) g (x)
I
f (x) = sin(x2+3x+8) f (x) = cos(x2+3x+8) (2x+3)
I
f (x) = sin(ex + x3) f (x) = cos(ex + x3) (ex +3x2)
I
f (x) = sin(ln(x)) f (x) = cos(ln(x)) 1x
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Ejemplos:
f (x) = sin(g(x)) f (x) = cos(g(x)) g (x)
If (x) = sin(x2+3x+8)
f (x) = cos(x2+3x+8) (2x+3)
I
f (x) = sin(ex + x3) f (x) = cos(ex + x3) (ex +3x2)
I
f (x) = sin(ln(x)) f (x) = cos(ln(x)) 1x
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Ejemplos:
f (x) = sin(g(x)) f (x) = cos(g(x)) g (x)
If (x) = sin(x2+3x+8) f (x) = cos(x2+3x+8) (2x+3)
I
f (x) = sin(ex + x3) f (x) = cos(ex + x3) (ex +3x2)
I
f (x) = sin(ln(x)) f (x) = cos(ln(x)) 1x
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Ejemplos:
f (x) = sin(g(x)) f (x) = cos(g(x)) g (x)
If (x) = sin(x2+3x+8) f (x) = cos(x2+3x+8) (2x+3)
If (x) = sin(ex + x3)
f (x) = cos(ex + x3) (ex +3x2)
I
f (x) = sin(ln(x)) f (x) = cos(ln(x)) 1x
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Ejemplos:
f (x) = sin(g(x)) f (x) = cos(g(x)) g (x)
If (x) = sin(x2+3x+8) f (x) = cos(x2+3x+8) (2x+3)
If (x) = sin(ex + x3) f (x) = cos(ex + x3) (ex +3x2)
I
f (x) = sin(ln(x)) f (x) = cos(ln(x)) 1x
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Ejemplos:
f (x) = sin(g(x)) f (x) = cos(g(x)) g (x)
If (x) = sin(x2+3x+8) f (x) = cos(x2+3x+8) (2x+3)
If (x) = sin(ex + x3) f (x) = cos(ex + x3) (ex +3x2)
If (x) = sin(ln(x))
f (x) = cos(ln(x)) 1x
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Ejemplos:
f (x) = sin(g(x)) f (x) = cos(g(x)) g (x)
If (x) = sin(x2+3x+8) f (x) = cos(x2+3x+8) (2x+3)
If (x) = sin(ex + x3) f (x) = cos(ex + x3) (ex +3x2)
If (x) = sin(ln(x)) f (x) = cos(ln(x)) 1x
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Ejemplos:
f (x) = cos(g(x)) f (x) =sin(g(x)) g (x)
I
f (x) = cos(x3+3x2) f (x) =sin(x3+3x2) (3x2+6x)
I
f (x) = cos(3ex + x) f (x) =sin(3ex + x) (3ex +1)
I
f (x) = cos(3 ln(x)) f (x) =sin(3 ln(x)) 3x
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Ejemplos:
f (x) = cos(g(x))
f (x) =sin(g(x)) g (x)
I
f (x) = cos(x3+3x2) f (x) =sin(x3+3x2) (3x2+6x)
I
f (x) = cos(3ex + x) f (x) =sin(3ex + x) (3ex +1)
I
f (x) = cos(3 ln(x)) f (x) =sin(3 ln(x)) 3x
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Ejemplos:
f (x) = cos(g(x)) f (x) =sin(g(x)) g (x)
I
f (x) = cos(x3+3x2) f (x) =sin(x3+3x2) (3x2+6x)
I
f (x) = cos(3ex + x) f (x) =sin(3ex + x) (3ex +1)
I
f (x) = cos(3 ln(x)) f (x) =sin(3 ln(x)) 3x
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Ejemplos:
f (x) = cos(g(x)) f (x) =sin(g(x)) g (x)
If (x) = cos(x3+3x2)
f (x) =sin(x3+3x2) (3x2+6x)
I
f (x) = cos(3ex + x) f (x) =sin(3ex + x) (3ex +1)
I
f (x) = cos(3 ln(x)) f (x) =sin(3 ln(x)) 3x
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Ejemplos:
f (x) = cos(g(x)) f (x) =sin(g(x)) g (x)
If (x) = cos(x3+3x2) f (x) =sin(x3+3x2) (3x2+6x)
I
f (x) = cos(3ex + x) f (x) =sin(3ex + x) (3ex +1)
I
f (x) = cos(3 ln(x)) f (x) =sin(3 ln(x)) 3x
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Ejemplos:
f (x) = cos(g(x)) f (x) =sin(g(x)) g (x)
If (x) = cos(x3+3x2) f (x) =sin(x3+3x2) (3x2+6x)
If (x) = cos(3ex + x)
f (x) =sin(3ex + x) (3ex +1)
I
f (x) = cos(3 ln(x)) f (x) =sin(3 ln(x)) 3x
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Ejemplos:
f (x) = cos(g(x)) f (x) =sin(g(x)) g (x)
If (x) = cos(x3+3x2) f (x) =sin(x3+3x2) (3x2+6x)
If (x) = cos(3ex + x) f (x) =sin(3ex + x) (3ex +1)
I
f (x) = cos(3 ln(x)) f (x) =sin(3 ln(x)) 3x
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Ejemplos:
f (x) = cos(g(x)) f (x) =sin(g(x)) g (x)
If (x) = cos(x3+3x2) f (x) =sin(x3+3x2) (3x2+6x)
If (x) = cos(3ex + x) f (x) =sin(3ex + x) (3ex +1)
If (x) = cos(3 ln(x))
f (x) =sin(3 ln(x)) 3x
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Ejemplos:
f (x) = cos(g(x)) f (x) =sin(g(x)) g (x)
If (x) = cos(x3+3x2) f (x) =sin(x3+3x2) (3x2+6x)
If (x) = cos(3ex + x) f (x) =sin(3ex + x) (3ex +1)
If (x) = cos(3 ln(x)) f (x) =sin(3 ln(x)) 3x
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Ejemplos:
f (x) = tan(g(x)) f (x) = (1+ tan2(g(x))) g (x)
I
f (x) = tan(5x4) f (x) = (1+ tan2 (5x4)) (20x3)
I
f (x) = tan(x) f (x) = (1+ tan2 (x)) ( 12
x
)
I
f (x) = tan(cos(x)) f (x) = (1+ tan2 (cos(x))) (sin(x))
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Ejemplos:
f (x) = tan(g(x))
f (x) = (1+ tan2(g(x))) g (x)
I
f (x) = tan(5x4) f (x) = (1+ tan2 (5x4)) (20x3)
I
f (x) = tan(x) f (x) = (1+ tan2 (x)) ( 12
x
)
I
f (x) = tan(cos(x)) f (x) = (1+ tan2 (cos(x))) (sin(x))
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Ejemplos:
f (x) = tan(g(x)) f (x) = (1+ tan2(g(x))) g (x)
I
f (x) = tan(5x4) f (x) = (1+ tan2 (5x4)) (20x3)
I
f (x) = tan(x) f (x) = (1+ tan2 (x)) ( 12
x
)
I
f (x) = tan(cos(x)) f (x) = (1+ tan2 (cos(x))) (sin(x))
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Ejemplos:
f (x) = tan(g(x)) f (x) = (1+ tan2(g(x))) g (x)
If (x) = tan(5x4)
f (x) = (1+ tan2 (5x4)) (20x3)
I
f (x) = tan(x) f (x) = (1+ tan2 (x)) ( 12
x
)
I
f (x) = tan(cos(x)) f (x) = (1+ tan2 (cos(x))) (sin(x))
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Ejemplos:
f (x) = tan(g(x)) f (x) = (1+ tan2(g(x))) g (x)
If (x) = tan(5x4) f (x) = (1+ tan2 (5x4)) (20x3)
I
f (x) = tan(x) f (x) = (1+ tan2 (x)) ( 12
x
)
I
f (x) = tan(cos(x)) f (x) = (1+ tan2 (cos(x))) (sin(x))
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Ejemplos:
f (x) = tan(g(x)) f (x) = (1+ tan2(g(x))) g (x)
If (x) = tan(5x4) f (x) = (1+ tan2 (5x4)) (20x3)
If (x) = tan(
x)
f (x) = (1+ tan2 (x)) ( 12
x
)
I
f (x) = tan(cos(x)) f (x) = (1+ tan2 (cos(x))) (sin(x))
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Ejemplos:
f (x) = tan(g(x)) f (x) = (1+ tan2(g(x))) g (x)
If (x) = tan(5x4) f (x) = (1+ tan2 (5x4)) (20x3)
If (x) = tan(
x) f (x) = (1+ tan2 (x)) ( 12
x
)
I
f (x) = tan(cos(x)) f (x) = (1+ tan2 (cos(x))) (sin(x))
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Ejemplos:
f (x) = tan(g(x)) f (x) = (1+ tan2(g(x))) g (x)
If (x) = tan(5x4) f (x) = (1+ tan2 (5x4)) (20x3)
If (x) = tan(
x) f (x) = (1+ tan2 (x)) ( 12
x
)
If (x) = tan(cos(x))
f (x) = (1+ tan2 (cos(x))) (sin(x))
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Ejemplos:
f (x) = tan(g(x)) f (x) = (1+ tan2(g(x))) g (x)
If (x) = tan(5x4) f (x) = (1+ tan2 (5x4)) (20x3)
If (x) = tan(
x) f (x) = (1+ tan2 (x)) ( 12
x
)
If (x) = tan(cos(x)) f (x) = (1+ tan2 (cos(x))) (sin(x))
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Repaso:
IClculo de derivadas de funciones
trigonomtricas compuestas